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- 1. Introduction to Statistical Quality Control
- 2. The contents of SQC • Meaning statistical process control • Control charts for variables – R chart, ⎯X chart • Control charts for attributes – P chart, nP chart and c chart • Acceptance sampling – Producer’s & consumer’s risk
- 3. Statistical Quality Control (SQC) • Uses mathematics (i.e., statistics) • Involves collecting data, organizing & interpreting those collected data • Objective: To Regulate product quality • These are Used to – Control the process as and when the products are produced, and – Inspect samples of finished products
- 4. Types of Statistical Quality Control
- 5. • Characteristics for which one focuses on defects • Classify products as either ‘good’ or ‘bad’, or count # defects – e.g., radio works or not • Categorical or discrete random variables Attributes Attributes Quality Characteristics • Characteristics that one can measure – e.g., weight, length • May be whole number or fractional • Continuous random variables Variables Variables
- 6. Statistical Process Control
- 7. Statistical Process Control (SPC) • Statistical technique used to ensure that the process is making product to standard • All process are subject to variability – Natural causes: Random or chance variations – Assignable causes: Correctable problems • Machine wear, unskilled workers, poor mat’l • Objective: Identify assignable causes • Uses process control charts
- 8. Purpose of Control Chart • Show changes in data pattern – e.g., trends • Make corrections before process is out of control • Show causes of changes in data – Assignable causes • Data outside control limits or trend in data – Natural causes • Random variations around average
- 9. Statistical Process Control Steps
- 10. Types of Control Chart R X P C R X P C Continuous Continuous Numerical Data Numerical Data Categorical or Categorical or Discrete Numerical Discrete Numerical Data Data
- 11. R Chart
- 12. R Chart • Type of variables control chart – Interval or ratio scaled numerical data • Shows sample ranges over time – Difference between smallest & largest values in inspection sample • Monitors variability in process • Example: Weigh samples of coffee & compute ranges of samples; Plot
- 13. R &⎯X Chart Hotel Data R &⎯X Chart Hotel Data Sample Day Delivery Time Mean Range 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 7.30 7.30 - - 3.45 3.45 Sample Range = Sample Range = Largest Largest Smallest Smallest
- 14. R &⎯X Chart Hotel Data Sample Day Delivery Time Mean Range 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27 3 5.98 2.92 6.20 4.20 5.10 4.88 3.28 4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22
- 15. ⎯X Chart • Type of variables control chart – Interval or ratio scaled numerical data • Shows sample means over time • Monitors process average • Example: measure dimensions of samples of components & compute means of samples; & Plot the graph.
- 16. R &⎯X Chart Some Data Sample Day Delivery Time Mean Range 1 7.30 4.20 6.10 3.45 5.55 5.32 3.85 2 4.60 8.70 7.60 4.43 7.62 6.59 4.27 3 5.98 2.92 6.20 4.20 5.10 4.88 3.28 4 7.20 5.10 5.19 6.80 4.21 5.70 2.99 5 4.00 4.50 5.50 1.89 4.46 4.07 3.61 6 10.10 8.10 6.50 5.06 6.94 7.34 5.04 7 6.77 5.08 5.90 6.90 9.30 6.79 4.22
- 17. • Solution* • Redesign the process • Use TQM tools – Cause & effect diagrams – Process flow charts – Pareto charts If the process is out of control Method Method People People Material Material Equipment Equipment Too Long
- 18. Acceptance Sampling
- 19. Statistical Quality Control
- 20. What Is Acceptance Sampling? • It is a “Form of quality testing” used for incoming materials or finished goods – e.g., purchased material & components • Procedure – Take one or more samples at random from a lot (shipment) of items – Inspect each of the items in the sample – Decide whether to reject the whole lot based on the inspection results
- 21. What Is an Acceptance Plan? • It is a “Set of procedure” for inspecting incoming materials or finished goods • It Identifies – Type of sample – Sample size (n) – Criteria (c) used to reject or accept a lot • Producer (supplier) & consumer (buyer) must negotiate
- 22. • Select a single random sample of size n = 40 bags of potatoes from a shipment (lot) of 200 bags. • Determine the sample mean weight,⎯X, of the 40 bags. • If⎯X ≥ 39.5 Kgs., accept the shipment (lot) of 200 bags; otherwise reject it & inspect all bags. Example Sampling Plan for Variables © 1995 Corel Corp.
- 23. Operating Characteristics Curve • Shows how well a sampling plan discriminates between good & bad lots (shipments) • Shows the relationship between the probability of accepting a lot & its quality
- 24. Producer’s & Consumer’s Risk • Producer's risk (α) – Probability of rejecting a good lot – Probability of rejecting a lot when fraction defective is AQL • Consumer's risk (ß) – Probability of accepting a bad lot – Probability of accepting a lot when fraction defective is LTPD